ISSUES RELATED TO THE PROBLEM

First of all, the problem is a bit intimidating with all the mechanical engineering jargon. It might be possible to state it purely as a mathematics problem, for example:

"Find a function of q which starting from zero rises to .1 at q=p/2, drops back to zero at q = p and has continuous first and second derivatives. The maximum absolute value of the second derivative should be as small as possible."

When the problem has been solved, then the student could be shown the mechanical engineering motivation. This seems to rob the problem of its challenge in some ways.

But, at heart, cam design is just curve fitting! See the reference.

The problem is an effort to find applications of the calculus in the engine of an automobile. An effort has been made to write it in a way that makes it accessible to students who have never had a course in mechanical engineering.

The problem ties in to the issues of continuity and differentiability of functions. As the principal law of cam design states, "The cam displacement function must have continuous first and second derivatives everywhere in its domain."

The problem is posed in a rather open-ended way. There are an infinite number of functions which fit the requirements. We want to find a good one!